In multi-rate filter bank applications (e.g. a wideband channelizer) where overlapping and non-overlapping 2D rectangular regions represent different frequency bands of interest at different times and over different time durations, different layers of frequency resolution can potentially generate overlaps causing multiple detection within one time-frequency cell. These time frequency overlaps result in less efficient compression due to multiple transmissions of the same data. Additionally since signal reconstruction errors increase for smaller time-frequency regions, the most accurate reconstruction corresponds to regions with the largest bandwidth and longest time-duration. FIG. 1 shows twenty exemplary 2D rectangular regions of interest showing the overlaps between different regions.
In binary image coding where the compressed data corresponding to just the locations and sizes of the non-zero “black” regions is sufficient for reconstructing the image, an iterative approach is used. Known methods of binary image coding consists of three main steps: (a) a raster-scan through the columns and then the rows of the image to find the next non-zero pixel corresponding to a top-left corner, (b) a column-wise scan to find the top-right corner at the first zero pixel and (c) a row-wise scan to find either the bottom-left or bottom-right corner corresponding to a zero pixel between the left and right sides or to a non-zero pixel in the columns directly outside the left and right sides. However, this method does not provide the set of non-overlapping regions with either maximum vertical-extent or maximum horizontal-extent. Also, the method cannot be directly applied to a set of overlapping rectangular regions to determine the optimal set of non-overlapping regions.
A known prior art compression technique for binary text images uses a similar approach. The prior art technique partitions the non-zero regions into non-overlapping and fully overlapping regions, defines the vertices and assigns specific codes to the converted rectangular regions' vertices reflective of their status as non-overlapping or fully overlapping regions. This method does not provide a set of non-overlapping rectangular regions encompassing the entire marked area, nor does it allow for a maximum extent in one dimension.
For data compression, error reduction, and other reasons, it is desirable to employ a method for converting overlapping rectangular two-dimensional (2D) regions into a new set of non-overlapping rectangular regions to thereby allow for efficient reconstruction of a signal output from the filter bank. It is further desirable that the above method determine the smallest set of non-overlapping rectangular regions with the maximum extent in either the vertical or the horizontal dimension since signal reconstruction errors are larger for smaller time-frequency regions. The most accurate reconstruction corresponds to regions with the largest bandwidth and longest time duration, i.e. larger time frequency regions.
Accordingly, it is an object of the disclosed subject matter to obviate many of the above problems in the prior art and to provide a novel method in a multi-channel detection system for transforming a plurality of overlapping two-dimensional rectangular regions into non-overlapping 2D rectangular regions wherein each non-overlapping region has a maximum extent in a major dimension (i.e. either horizontally or vertically). An embodiment of the method includes the steps of: splitting the overlapping regions into marked regions in a non-uniform grid; merging the marked grid regions along the major dimension and along the minor dimension to thereby form non-overlapping regions wherein no two non-overlapping rectangular regions have an adjacent edge orthogonal to the major dimension.
It is another object of the disclosed subject matter to provide a novel improvement of a method for compressing data. One embodiment of the method comprises the step of transforming overlapping two-dimensional rectangular regions into non-overlapping 2D rectangular regions wherein the non-overlapping rectangular regions have a maximum extent in one dimension.
It is yet another object of the disclosed subject matter to provide, in a time-frequency window of interest, a novel method of excising the overlapping portion of two-dimensional rectangular areas. An embodiment of the method comprises the steps of forming a non-uniform two-dimensional grid using the coordinates of the overlapping rectangular areas; splitting the overlapping 2D rectangular areas into non-uniform grid units, and combining adjacent tagged grid units into non-overlapping rectangular regions defined by major edges and minor corners.
It is still another object of the disclosed subject matter to provide a novel method of reconstructing a coverage area defined by overlapping two-dimensional rectangular regions with non-overlapping 2D rectangular regions. An embodiment of the method comprises the steps of forming a non-uniform two-dimensional grid using the coordinates of the overlapping rectangular areas; splitting the overlapping 2D rectangular areas into non-uniform grid units; and combining adjacent tagged grid units into non-overlapping rectangular regions defined by major edges and minor corners.
It is an additional object of the disclosed subject matter to provide a novel improvement for a method in a Cartesian space defined by a frequency domain and a time domain for transforming a plurality of overlapping rectangular regions into a plurality of non-overlapping rectangular regions. An embodiment of the method comprises the improvement wherein none of the non-overlapping rectangular regions share a common edge orthogonal to a preferred dimension.
It is still an additional object of the disclosed subject matter to provide, in a time-frequency window of interest, a novel method of excising the overlapping portion of overlapping two-dimensional rectangular areas comprising the step of transforming the overlapping rectangular areas into non-overlapping rectangular areas by the improvement wherein none of the non-overlapping rectangular areas share a common edge orthogonal to a preferred dimension.
These and many other objects and advantages of the disclosed subject matter will be readily apparent to one skilled in the art to which the disclosure pertains from a perusal or the claims, the appended drawings, and the following detailed description of the preferred embodiments.